Theorem 1.1 (Theorem A of [1]})
Let \(\pi \)  be an irreducible (\(\mathfrak {g}\) , \(K\) ) module with infinitesimal character \(\Lambda \) .
Assume that \(H_D(\pi )\ne 0\) , and let \(\gamma \in \mathfrak {t}_f^{*}\subset \mathfrak {h}_f^{*}\)  be any highest weight of any \(\widetilde{K}\) -type in it. Then \(\Lambda =w(\gamma +\rho _{c})\)  for some element \(w\in W(\mathfrak {g},\mathfrak {h}_f)\) .

